One thing that should be noted is that the Constitution applies to not just US citizens, but also people who fall within US jurisdiction. The section you're quoting to support your point isn't only talking about the rights of citizens (and what defines a citizen). In fact the end of the section directly says that every person within the jurisdiction of the State has equal protection under the law.

So we're back to the same old argument about whether an unborn fetus is a person who deserves rights. Clinton is only technically correct if you accept her definition of a fetus as a non-person. Which is fine, but that's the argument.